shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
1
vote
2answers
32 views
Show that the orthocenter must coincide with one of the vertices of triangle ABC.
Given the orthocenter and circumcenter both lie on the nine-point circle prove that the orthocenter must coincide with one of the vertices of triangle ABC.
I have already proved that the orthocenter ...
0
votes
1answer
11 views
To find a point in a horizontal plane to minimise the distance
A, B and C are three points in 3D space. The points A and B are fixed. C is below A and B. $H_{p}$ is any given plane.
Point C moves along the plane $H_{p}$.
How to find the location of point C ...
0
votes
1answer
15 views
Prove that X can't possibly be a point on side BC that coincides with the midpoint or the other point of intersection of the nine-point circle.
In a triangle ABC Let a point X be the point of tangency of the excircle opposite A with side BC. I am trying to prove the point X cannot cannot lie on the nine-point circle of triangle ABC. I proved ...
2
votes
1answer
41 views
Mapping random points on a sphere onto a uniform grid
Say I had an arbitrary sphere that is covered in a uniform triangle mesh of N elements with each element having a unique sequential index.
If given the coordinates of a random point on the surface of ...
1
vote
0answers
21 views
Convex cone as sum of simplices?
In 3D a pyramid with a square base can be decomposed into the sum of two tetrahedra, i.e. two 3-simplices.
I am dealing with a homogeneous N-dimensional system of inequalities and my solution is a ...
0
votes
2answers
34 views
Find the equation of a locus…(Read More)
Find the equation of the locus of a point which moves so that it's distance from (4,-3) is always one-half its distance from (-1,-1).
1
vote
2answers
30 views
How to find length when viewing at some angle?
I have a question on angles. I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some ...
1
vote
1answer
38 views
How to find length of a rectangular tile when viewing at some angle [duplicate]
I have a question on angles.
I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some ...
0
votes
1answer
31 views
Prove triangles with same perimeter and point of tangency of excircle and nine-point circle.
In triangle ABC let X be the point of tangency of the excircle opposite A with side BC. (A) Prove that the segment AX divides triangle ABC into two triangles, each having the same perimeter. (B) Prove ...
3
votes
1answer
29 views
calculate rotation from 2 3d lines
I am trying to extract the transformation of a segment described by two 3d points $(a_0,b_0)$ into the transformed points $(a_1,b_1)$.
I have been able to calculate the translation, and I am assuming ...
2
votes
1answer
29 views
How do I prove that the triangle must be obtuse?
Suppose you are given a triangle where the center of the nine-point circle lies on the circumcircle of the triangle. It is obvious that the triangle is obtuse, but how can you formally prove that the ...
1
vote
1answer
26 views
How to sketch the graph of $\varphi(X)=d(X,A)+d(X,B)$ when $A$ and $B$ are not given?
$A,B$ are points in an axis, disposed in this order. Sketch the graph
of the following function:
$$\varphi(X)=d(X,A)+d(X,B)$$
$d(A,B)$ is the distance from point $A$ to point $B$.
I'm ...
1
vote
1answer
19 views
Question about the dimension of the intersection of two subspaces of a vector space $V$.
Let $M, N$ be two subspaces of a vector space $V$ with dimension $k$. Suppose that $\dim M=m$, $\dim N =n$. It is said that $\dim M \cap N \geq m+n-k$. Suppose that $M, N$ are two parallel planes in ...
2
votes
1answer
29 views
The best softwares to understand the intersections of the 3D objects in the Euclidean space
What is the best software (Easy to follow and clear graphics) to draw the intersections between two spheres, Two spheres and a pyramid, for example.
The centre and the radius of the spheres are given ...
0
votes
2answers
54 views
If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.
Thanks in advance to anyone who can help me out on this. I'm currently a junior in high school taking and doing well my school's honors pre-calc class, but of all of the math I've ever learned, proofs ...
0
votes
3answers
64 views
Distance between two antennas
I am trying to find out the formula to calculate how high antennas need to be for Line of Sight (LoS) propagation.
I found:
d = 3.57sqrt(h)
also
...
2
votes
3answers
64 views
Permutations and Cross-ratios
Pick four distinct numbers, list all 24 permutations, and compute the cross-ratio of each permutation. Show that at most six numbers have occurred, given by the cross-ratio group
$y, \frac{1}{y}, 1-y, ...
1
vote
2answers
47 views
Constructing Points
Given that you have two lines intersecting at the origin "0", with the unit "1" marked on each line, and "2" marked on the second line, clearly show how you would construct the point (2+1), the point ...
1
vote
2answers
48 views
Showing that f cannot be a linear fractional transformation
Let $f(x) = \frac{x^2}{x+1}$. Show that f cannot be a linear fractional transformation. (Hint: do not try to argue that f cannot be put into the form of $\frac{ax+b}{cx+d}$).
-1
votes
0answers
30 views
Generating Linear Fractional Transformations
Let $f(x)$ be a linear fractional transformation of your choosing, as long as $a, b, c, d \neq 0$ and $ad-bc \neq 0$.
i) Express $f(x)$ as a composition of generating transformations.
ii) Pick four ...
1
vote
1answer
50 views
Limits of the Minkowski distance as related to the generalized mean
Given that the Minkowski distance is $$d(X=(x_1,...,x_n),Y=(y_1,...,y_n))=(\sum_{i=1}^n|x_i−y_i|^p)^{1/p}$$ I understand that $$\lim_{p\to\infty}d(X,Y)=\max_{i=1}^n|x_i-y_i|$$ ...
0
votes
1answer
19 views
Given two lat/long/altitude points, how do I find the north/east/up vector between the two points?
I have two lat/long/altitude points $(\phi_1,\lambda_1,h_1)$ and $(\phi_2,\lambda_2,h_2)$. I wanted to find the distances in the east and north directions (up is fairly obvious, I think?) between ...
1
vote
0answers
23 views
maximum length of a scaled vector in a triangle (simplex)
Given a triangle (or, in general, a simplex) $T$ and a vector $\vec{s}$, I'd like to compute the quantity
$$
\max\{|x-y|: x,y\in T, x-y = \alpha \vec{s}, \alpha\in\mathbb{R}\}
$$
i.e., the maximum ...
3
votes
1answer
86 views
contest problem in geometry
Suppose the inscribed circle of $\triangle A_1A_2A_3$ touches the sides $A_2A_3, A_3A_1, A_1A_2$ at $T_1,T_2,T_3$. From the midpoints $M_1,M_2,M_3$ of $A_2A_3,A_3A_1,A_1A_2$, draw lines perpendicular ...
0
votes
3answers
62 views
Finding mass of a sphere whose density is given
I want to find the mass of a sphere of radius $a$ whose density at a point is proportional to the distance of a point from a plane passing through a diameter of a sphere
0
votes
1answer
23 views
equation of a plane passing through a diameter of a sphere
I want to find the equation of plane passing through a diameter of a sphere, For simplicity let us assume that origin,$(0,0,1)$ and $(0,0,-1)$ are on a diameter, then the points lie on the plane ...
-1
votes
0answers
25 views
Imaginary line passing through non-collinear points in R3.
I have come to a problem where n points are provided in 3-Dimensional plane. I need a imaginary line which can be assumed that it is passing through these points.
7
votes
3answers
70 views
Equation of Cone vs Elliptic Paraboloid
I can't understand why $$\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2} \tag{*}$$ corresponds to an elliptic paraboloid and $$\frac{z^2}{c^2} = \frac{x^2}{a^2} + \frac{y^2}{b^2} \tag{**}$$ to a cone, ...
4
votes
0answers
43 views
Good textbooks on Non-Euclidean Geometry?
I'm currently taking a class called Foundations of Geometry. We started with the stereographic projection and carried onward through fractional linear transformations, and now we are working with the ...
2
votes
1answer
32 views
Problem with finding the intersection point between a line and triangle
I have a mathematical problem that I'm trying to solve, but the equations I have derived don't give the correct output when utilised on concrete problems. However, I can't figure out what the problem ...
4
votes
2answers
56 views
Looking for a (nonlinear) map from n-dimensional cube to an n-dimensional simplex
I am looking for a (nonlinear) map from n-dimensional cube to an n-dimensional simplex; to make it simple, assume the following figure which is showing a sample transformation for the case when $n=2$. ...
2
votes
2answers
65 views
A part of an I.M.O problem
Let $a$ be the base of a triangle and $a+b$ be its perimeter. Using the fact that area of triangle is maximum when the other two sides are equal, prove that among all quadrilaterals with fixed ...
0
votes
1answer
46 views
Calculate new positon of rectangle corners based on angle.
I am trying to make a re-sizable touch view with rotation in android. I re-size rectangle successfully. You can find code here
It has 4 corners. You can re-size that rectangle by dragging one of ...
5
votes
0answers
59 views
Does this graph have a name?
Does graph shown below from the paper Dissection Graphs of Planar Point Sets by P. Erdos, L. Lovasz, A. Simmons, and E.G. Straus have a name?
Does it come from a family of related graphs?
0
votes
1answer
49 views
Length of DNA strand
The DNA molecule has a double helix structure. The radius of each helix is approximately $10$ angstroms ($1$ angstrom $=10^{-8}$cm). Each helix goes up by approximately $34$ angstroms every ...
1
vote
0answers
28 views
A rectangular prism has the surface area of 300 square inches. what whole number dimensions will give the prism the greatest volume. [duplicate]
it is a tough geometrical algebra problem
It is tough and involves geometry and algebra.
thank you
5
votes
1answer
243 views
Maximizing the volume of a rectangular prism
A rectangular prism has a surface area of $300$ square inches. What whole number dimensions give the prism the greatest volume?
This is a math olympiad problem. It involves the volume and surface ...
3
votes
3answers
37 views
Problem with determining cylinder height
Here is a question that I have, but I have no idea where to do go from here. Here is the question:
The vase company designs a new vase that is shaped like a cylinder on the bottom with a cone on ...
0
votes
1answer
19 views
How to I calculate a second plot point given the first point and the slope?
Is there a formula to calculate the second point in a segment given a starting point, segment length, and slope?
Thanks
0
votes
3answers
40 views
Please help me find a formula to find the 3rd point in a right triangle
I'm trying to figure out how to plot a 3rd point on a graph
Given the following line segments and angles
Is there a formula for the 3rd point?
Note: This image is just for an example. The base ...
1
vote
1answer
50 views
If I have three points on a circle, how do I calculate other points on the same circle?
I have circle which I know intersects the x axis at -11.5 and 11.5. It intersects the Y axis at 1. How can I calculate the (positive) Y value for any X value between -11.5 and 11.5?
This is to ...
0
votes
1answer
25 views
finding an equation through these two points in upper half plane
I have to find an equation going through $(-1,y)$ and $(1,y)$. The equation my book uses is $x^2+y^2+ax=b$. So I get two equations when I plug in the two points. I get $1+y^2-a=b$ and $1+y^2+a=b$ ...
1
vote
1answer
27 views
Please help me to find an equation to find the 3rd point in an arc.
Long story short, I want to animate the rotation of an object that's based off a circle.
Given the center point of the circle, the radius, and one of the points in the arc, is it possible to find the ...
3
votes
3answers
65 views
Parametric equation of an ellipse
How do I show that the parametric equations
$$x(t) = \sin(t+a)$$
$$y(t) = \sin(t+b)$$
define an ellipse?
I tried graphing it and I'm certain it is a rotated ellipse.
My first idea is to write it ...
0
votes
0answers
61 views
Geometrical Inequality
Let $ABCD$ be a quadrilateral on the unit circle, and the diagonals
$AC$ and $BD$ intersects at $E$. If the shortest height of the
triangle $ACD$ equals the radius of the incircle of the triangle ...
6
votes
2answers
122 views
A concise distance problem
A falsely simple Euclidian geometry problem:
Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$.
What is the set of possible $\|AC\|$ ?
I'm after a concise answer, ...
5
votes
5answers
138 views
Does $e$ have a geometric representation? [duplicate]
Just like $\pi$ is the ratio of a circle's circumference to its diameter? I know that the tangent line to the function $e^x$ has a slope of $e^x$ at that point, but is there some other geometric ...
1
vote
1answer
71 views
circle of inversion
Determine the equation of the circle reflection of the line $x = 2$ if the
circle of reflection is $x^2 + y^2 + 2x = 0$ which in standard form is $(x+1)^2+y^2=1$ where $radius=1$ and center is ...
2
votes
1answer
51 views
Center of circle that has two points on its circumference and a known tangent
I've found a related question, which helped me get started on this. I can get it to work for the example on the question, but I'm running into an issue when the tangent is not y = 0.
Other question ...
0
votes
1answer
21 views
Condition for a quadrilateral to be tangential
Define a quadrilateral to be tangential iff all four of its internal angle bisectors meet a a single point. Prove the following:
A quadrilateral is tangential if and only if three of of its ...
